Is Probability Space Nonlinear? Rachael L. Bond 1 , Thomas C. Ormerod 1 , Yang-Hui He 2,3,4 1 University of Sussex 2 City, University of London 3 Merton College, University of Oxford 4 NanKai University, P.R. China This article presents a new interpretation of the structure of subjective Bayesian probability spaces. Rather than assuming the linear space of classical statistical theory, it is proposed that Bayes’ theorem demands a curved, nonlinear probability space. This finding challenges over 250 years of accepted assumptions about Bayes Theorem and necessitates a re-evaluation of the reliability of any scientific research that relies upon it, whether that be in Psychology, Medicine, Informatics, Economics or the Physical Sciences. Bayes’ theorem is an expression that calculates a likelihood for conditionalised events, being used widely in fields as diverse as Medicine, Psychology, Machine Learning, Quantum Mechanics, Astrophysics, and general Statistics 1 . Often presented in the form (1), Bayes’ theorem describes the probability of an 1